LMFDB - Embedded newform 6010.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.293003$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.706997 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.706997 q^{6} -2.05365 q^{7} +1.00000 q^{8} -2.50015 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.706997 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.706997 q^{6} -2.05365 q^{7} +1.00000 q^{8} -2.50015 q^{9} +1.00000 q^{10} +5.00436 q^{11} -0.706997 q^{12} +1.44319 q^{13} -2.05365 q^{14} -0.706997 q^{15} +1.00000 q^{16} -5.11077 q^{17} -2.50015 q^{18} -0.185021 q^{19} +1.00000 q^{20} +1.45192 q^{21} +5.00436 q^{22} -2.44691 q^{23} -0.706997 q^{24} +1.00000 q^{25} +1.44319 q^{26} +3.88859 q^{27} -2.05365 q^{28} -2.29010 q^{29} -0.706997 q^{30} -9.99830 q^{31} +1.00000 q^{32} -3.53807 q^{33} -5.11077 q^{34} -2.05365 q^{35} -2.50015 q^{36} -5.58316 q^{37} -0.185021 q^{38} -1.02033 q^{39} +1.00000 q^{40} +2.67087 q^{41} +1.45192 q^{42} +2.86150 q^{43} +5.00436 q^{44} -2.50015 q^{45} -2.44691 q^{46} -1.49218 q^{47} -0.706997 q^{48} -2.78253 q^{49} +1.00000 q^{50} +3.61330 q^{51} +1.44319 q^{52} +9.86709 q^{53} +3.88859 q^{54} +5.00436 q^{55} -2.05365 q^{56} +0.130809 q^{57} -2.29010 q^{58} -9.79527 q^{59} -0.706997 q^{60} +1.70579 q^{61} -9.99830 q^{62} +5.13444 q^{63} +1.00000 q^{64} +1.44319 q^{65} -3.53807 q^{66} -4.31306 q^{67} -5.11077 q^{68} +1.72996 q^{69} -2.05365 q^{70} -10.7214 q^{71} -2.50015 q^{72} -1.68245 q^{73} -5.58316 q^{74} -0.706997 q^{75} -0.185021 q^{76} -10.2772 q^{77} -1.02033 q^{78} +3.43628 q^{79} +1.00000 q^{80} +4.75124 q^{81} +2.67087 q^{82} +0.478299 q^{83} +1.45192 q^{84} -5.11077 q^{85} +2.86150 q^{86} +1.61909 q^{87} +5.00436 q^{88} -7.20336 q^{89} -2.50015 q^{90} -2.96380 q^{91} -2.44691 q^{92} +7.06877 q^{93} -1.49218 q^{94} -0.185021 q^{95} -0.706997 q^{96} -4.23091 q^{97} -2.78253 q^{98} -12.5117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.706997	−0.408185	−0.204093	−	0.978952i	$-0.565424\pi$
$3$	−0.706997	−0.408185	−0.204093	+	0.978952i	$0.565424\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.706997	−0.288630
$7$	−2.05365	−0.776206	−0.388103	−	0.921616i	$-0.626870\pi$
$7$	−2.05365	−0.776206	−0.388103	+	0.921616i	$0.626870\pi$
$8$	1.00000	0.353553
$9$	−2.50015	−0.833385
$10$	1.00000	0.316228
$11$	5.00436	1.50887	0.754435	−	0.656375i	$-0.227911\pi$
$11$	5.00436	1.50887	0.754435	+	0.656375i	$0.227911\pi$
$12$	−0.706997	−0.204093
$13$	1.44319	0.400268	0.200134	−	0.979769i	$-0.435862\pi$
$13$	1.44319	0.400268	0.200134	+	0.979769i	$0.435862\pi$
$14$	−2.05365	−0.548860
$15$	−0.706997	−0.182546
$16$	1.00000	0.250000
$17$	−5.11077	−1.23954	−0.619772	−	0.784782i	$-0.712775\pi$
$17$	−5.11077	−1.23954	−0.619772	+	0.784782i	$0.712775\pi$
$18$	−2.50015	−0.589292
$19$	−0.185021	−0.0424467	−0.0212234	−	0.999775i	$-0.506756\pi$
$19$	−0.185021	−0.0424467	−0.0212234	+	0.999775i	$0.506756\pi$
$20$	1.00000	0.223607
$21$	1.45192	0.316836
$22$	5.00436	1.06693
$23$	−2.44691	−0.510217	−0.255108	−	0.966912i	$-0.582111\pi$
$23$	−2.44691	−0.510217	−0.255108	+	0.966912i	$0.582111\pi$
$24$	−0.706997	−0.144315
$25$	1.00000	0.200000
$26$	1.44319	0.283032
$27$	3.88859	0.748360
$28$	−2.05365	−0.388103
$29$	−2.29010	−0.425260	−0.212630	−	0.977133i	$-0.568203\pi$
$29$	−2.29010	−0.425260	−0.212630	+	0.977133i	$0.568203\pi$
$30$	−0.706997	−0.129079
$31$	−9.99830	−1.79575	−0.897874	−	0.440253i	$-0.854889\pi$
$31$	−9.99830	−1.79575	−0.897874	+	0.440253i	$0.854889\pi$
$32$	1.00000	0.176777
$33$	−3.53807	−0.615898
$34$	−5.11077	−0.876490
$35$	−2.05365	−0.347130
$36$	−2.50015	−0.416692
$37$	−5.58316	−0.917866	−0.458933	−	0.888471i	$-0.651768\pi$
$37$	−5.58316	−0.917866	−0.458933	+	0.888471i	$0.651768\pi$
$38$	−0.185021	−0.0300144
$39$	−1.02033	−0.163383
$40$	1.00000	0.158114
$41$	2.67087	0.417120	0.208560	−	0.978010i	$-0.433122\pi$
$41$	2.67087	0.417120	0.208560	+	0.978010i	$0.433122\pi$
$42$	1.45192	0.224037
$43$	2.86150	0.436374	0.218187	−	0.975907i	$-0.429986\pi$
$43$	2.86150	0.436374	0.218187	+	0.975907i	$0.429986\pi$
$44$	5.00436	0.754435
$45$	−2.50015	−0.372701
$46$	−2.44691	−0.360778
$47$	−1.49218	−0.217657	−0.108829	−	0.994061i	$-0.534710\pi$
$47$	−1.49218	−0.217657	−0.108829	+	0.994061i	$0.534710\pi$
$48$	−0.706997	−0.102046
$49$	−2.78253	−0.397504
$50$	1.00000	0.141421
$51$	3.61330	0.505963
$52$	1.44319	0.200134
$53$	9.86709	1.35535	0.677675	−	0.735362i	$-0.262988\pi$
$53$	9.86709	1.35535	0.677675	+	0.735362i	$0.262988\pi$
$54$	3.88859	0.529171
$55$	5.00436	0.674787
$56$	−2.05365	−0.274430
$57$	0.130809	0.0173261
$58$	−2.29010	−0.300704
$59$	−9.79527	−1.27524	−0.637618	−	0.770353i	$-0.720080\pi$
$59$	−9.79527	−1.27524	−0.637618	+	0.770353i	$0.720080\pi$
$60$	−0.706997	−0.0912730
$61$	1.70579	0.218404	0.109202	−	0.994020i	$-0.465170\pi$
$61$	1.70579	0.218404	0.109202	+	0.994020i	$0.465170\pi$
$62$	−9.99830	−1.26979
$63$	5.13444	0.646878
$64$	1.00000	0.125000
$65$	1.44319	0.179005
$66$	−3.53807	−0.435506
$67$	−4.31306	−0.526924	−0.263462	−	0.964670i	$-0.584864\pi$
$67$	−4.31306	−0.526924	−0.263462	+	0.964670i	$0.584864\pi$
$68$	−5.11077	−0.619772
$69$	1.72996	0.208263
$70$	−2.05365	−0.245458
$71$	−10.7214	−1.27239	−0.636196	−	0.771527i	$-0.719493\pi$
$71$	−10.7214	−1.27239	−0.636196	+	0.771527i	$0.719493\pi$
$72$	−2.50015	−0.294646
$73$	−1.68245	−0.196916	−0.0984579	−	0.995141i	$-0.531391\pi$
$73$	−1.68245	−0.196916	−0.0984579	+	0.995141i	$0.531391\pi$
$74$	−5.58316	−0.649029
$75$	−0.706997	−0.0816370
$76$	−0.185021	−0.0212234
$77$	−10.2772	−1.17119
$78$	−1.02033	−0.115529
$79$	3.43628	0.386612	0.193306	−	0.981139i	$-0.438079\pi$
$79$	3.43628	0.386612	0.193306	+	0.981139i	$0.438079\pi$
$80$	1.00000	0.111803
$81$	4.75124	0.527915
$82$	2.67087	0.294948
$83$	0.478299	0.0525001	0.0262501	−	0.999655i	$-0.491643\pi$
$83$	0.478299	0.0525001	0.0262501	+	0.999655i	$0.491643\pi$
$84$	1.45192	0.158418
$85$	−5.11077	−0.554341
$86$	2.86150	0.308563
$87$	1.61909	0.173585
$88$	5.00436	0.533466
$89$	−7.20336	−0.763555	−0.381777	−	0.924254i	$-0.624688\pi$
$89$	−7.20336	−0.763555	−0.381777	+	0.924254i	$0.624688\pi$
$90$	−2.50015	−0.263539
$91$	−2.96380	−0.310690
$92$	−2.44691	−0.255108
$93$	7.06877	0.732997
$94$	−1.49218	−0.153907
$95$	−0.185021	−0.0189828
$96$	−0.706997	−0.0721576
$97$	−4.23091	−0.429584	−0.214792	−	0.976660i	$-0.568907\pi$
$97$	−4.23091	−0.429584	−0.214792	+	0.976660i	$0.568907\pi$
$98$	−2.78253	−0.281078
$99$	−12.5117	−1.25747
$100$	1.00000	0.100000
$101$	4.22384	0.420288	0.210144	−	0.977670i	$-0.432607\pi$
$101$	4.22384	0.420288	0.210144	+	0.977670i	$0.432607\pi$
$102$	3.61330	0.357770
$103$	−1.25399	−0.123560	−0.0617798	−	0.998090i	$-0.519678\pi$
$103$	−1.25399	−0.123560	−0.0617798	+	0.998090i	$0.519678\pi$
$104$	1.44319	0.141516
$105$	1.45192	0.141693
$106$	9.86709	0.958377
$107$	13.0482	1.26141	0.630707	−	0.776021i	$-0.282765\pi$
$107$	13.0482	1.26141	0.630707	+	0.776021i	$0.282765\pi$
$108$	3.88859	0.374180
$109$	−3.61976	−0.346710	−0.173355	−	0.984859i	$-0.555461\pi$
$109$	−3.61976	−0.346710	−0.173355	+	0.984859i	$0.555461\pi$
$110$	5.00436	0.477147
$111$	3.94728	0.374659
$112$	−2.05365	−0.194051
$113$	6.27803	0.590588	0.295294	−	0.955406i	$-0.404582\pi$
$113$	6.27803	0.590588	0.295294	+	0.955406i	$0.404582\pi$
$114$	0.130809	0.0122514
$115$	−2.44691	−0.228176
$116$	−2.29010	−0.212630
$117$	−3.60819	−0.333577
$118$	−9.79527	−0.901728
$119$	10.4957	0.962141
$120$	−0.706997	−0.0645397
$121$	14.0436	1.27669
$122$	1.70579	0.154435
$123$	−1.88830	−0.170262
$124$	−9.99830	−0.897874
$125$	1.00000	0.0894427
$126$	5.13444	0.457412
$127$	22.1156	1.96244	0.981221	−	0.192886i	$-0.0617848\pi$
$127$	22.1156	1.96244	0.981221	+	0.192886i	$0.0617848\pi$
$128$	1.00000	0.0883883
$129$	−2.02307	−0.178121
$130$	1.44319	0.126576
$131$	−11.9713	−1.04594	−0.522968	−	0.852352i	$-0.675175\pi$
$131$	−11.9713	−1.04594	−0.522968	+	0.852352i	$0.675175\pi$
$132$	−3.53807	−0.307949
$133$	0.379968	0.0329474
$134$	−4.31306	−0.372592
$135$	3.88859	0.334677
$136$	−5.11077	−0.438245
$137$	−23.0925	−1.97292	−0.986462	−	0.163988i	$-0.947564\pi$
$137$	−23.0925	−1.97292	−0.986462	+	0.163988i	$0.947564\pi$
$138$	1.72996	0.147264
$139$	−13.6405	−1.15697	−0.578487	−	0.815691i	$-0.696357\pi$
$139$	−13.6405	−1.15697	−0.578487	+	0.815691i	$0.696357\pi$
$140$	−2.05365	−0.173565
$141$	1.05497	0.0888444
$142$	−10.7214	−0.899717
$143$	7.22222	0.603952
$144$	−2.50015	−0.208346
$145$	−2.29010	−0.190182
$146$	−1.68245	−0.139241
$147$	1.96724	0.162255
$148$	−5.58316	−0.458933
$149$	−1.26679	−0.103780	−0.0518899	−	0.998653i	$-0.516524\pi$
$149$	−1.26679	−0.103780	−0.0518899	+	0.998653i	$0.516524\pi$
$150$	−0.706997	−0.0577261
$151$	−8.57737	−0.698017	−0.349008	−	0.937120i	$-0.613482\pi$
$151$	−8.57737	−0.698017	−0.349008	+	0.937120i	$0.613482\pi$
$152$	−0.185021	−0.0150072
$153$	12.7777	1.03302
$154$	−10.2772	−0.828159
$155$	−9.99830	−0.803083
$156$	−1.02033	−0.0816917
$157$	−19.4496	−1.55225	−0.776124	−	0.630580i	$-0.782817\pi$
$157$	−19.4496	−1.55225	−0.776124	+	0.630580i	$0.782817\pi$
$158$	3.43628	0.273376
$159$	−6.97601	−0.553233
$160$	1.00000	0.0790569
$161$	5.02510	0.396033
$162$	4.75124	0.373293
$163$	−7.83300	−0.613528	−0.306764	−	0.951786i	$-0.599246\pi$
$163$	−7.83300	−0.613528	−0.306764	+	0.951786i	$0.599246\pi$
$164$	2.67087	0.208560
$165$	−3.53807	−0.275438
$166$	0.478299	0.0371232
$167$	11.9151	0.922014	0.461007	−	0.887396i	$-0.347488\pi$
$167$	11.9151	0.922014	0.461007	+	0.887396i	$0.347488\pi$
$168$	1.45192	0.112018
$169$	−10.9172	−0.839786
$170$	−5.11077	−0.391978
$171$	0.462581	0.0353745
$172$	2.86150	0.218187
$173$	7.26378	0.552255	0.276127	−	0.961121i	$-0.410949\pi$
$173$	7.26378	0.552255	0.276127	+	0.961121i	$0.410949\pi$
$174$	1.61909	0.122743
$175$	−2.05365	−0.155241
$176$	5.00436	0.377218
$177$	6.92523	0.520532
$178$	−7.20336	−0.539915
$179$	−3.07473	−0.229816	−0.114908	−	0.993376i	$-0.536657\pi$
$179$	−3.07473	−0.229816	−0.114908	+	0.993376i	$0.536657\pi$
$180$	−2.50015	−0.186351
$181$	−14.2293	−1.05765	−0.528827	−	0.848729i	$-0.677368\pi$
$181$	−14.2293	−1.05765	−0.528827	+	0.848729i	$0.677368\pi$
$182$	−2.96380	−0.219691
$183$	−1.20599	−0.0891493
$184$	−2.44691	−0.180389
$185$	−5.58316	−0.410482
$186$	7.06877	0.518307
$187$	−25.5761	−1.87031
$188$	−1.49218	−0.108829
$189$	−7.98580	−0.580882
$190$	−0.185021	−0.0134228
$191$	−26.0360	−1.88390	−0.941949	−	0.335755i	$-0.891008\pi$
$191$	−26.0360	−1.88390	−0.941949	+	0.335755i	$0.891008\pi$
$192$	−0.706997	−0.0510231
$193$	−15.7653	−1.13481	−0.567407	−	0.823438i	$-0.692053\pi$
$193$	−15.7653	−1.13481	−0.567407	+	0.823438i	$0.692053\pi$
$194$	−4.23091	−0.303762
$195$	−1.02033	−0.0730673
$196$	−2.78253	−0.198752
$197$	4.70772	0.335411	0.167706	−	0.985837i	$-0.446364\pi$
$197$	4.70772	0.335411	0.167706	+	0.985837i	$0.446364\pi$
$198$	−12.5117	−0.889165
$199$	−22.5777	−1.60049	−0.800245	−	0.599673i	$-0.795297\pi$
$199$	−22.5777	−1.60049	−0.800245	+	0.599673i	$0.795297\pi$
$200$	1.00000	0.0707107
$201$	3.04932	0.215083
$202$	4.22384	0.297188
$203$	4.70305	0.330089
$204$	3.61330	0.252982
$205$	2.67087	0.186542
$206$	−1.25399	−0.0873698
$207$	6.11766	0.425207
$208$	1.44319	0.100067
$209$	−0.925911	−0.0640466
$210$	1.45192	0.100192
$211$	10.5796	0.728326	0.364163	−	0.931335i	$-0.381355\pi$
$211$	10.5796	0.728326	0.364163	+	0.931335i	$0.381355\pi$
$212$	9.86709	0.677675
$213$	7.57998	0.519372
$214$	13.0482	0.891954
$215$	2.86150	0.195152
$216$	3.88859	0.264585
$217$	20.5330	1.39387
$218$	−3.61976	−0.245161
$219$	1.18949	0.0803781
$220$	5.00436	0.337394
$221$	−7.37579	−0.496149
$222$	3.94728	0.264924
$223$	2.98502	0.199892	0.0999458	−	0.994993i	$-0.468133\pi$
$223$	2.98502	0.199892	0.0999458	+	0.994993i	$0.468133\pi$
$224$	−2.05365	−0.137215
$225$	−2.50015	−0.166677
$226$	6.27803	0.417609
$227$	−0.464604	−0.0308368	−0.0154184	−	0.999881i	$-0.504908\pi$
$227$	−0.464604	−0.0308368	−0.0154184	+	0.999881i	$0.504908\pi$
$228$	0.130809	0.00866306
$229$	5.74517	0.379652	0.189826	−	0.981818i	$-0.439208\pi$
$229$	5.74517	0.379652	0.189826	+	0.981818i	$0.439208\pi$
$230$	−2.44691	−0.161345
$231$	7.26594	0.478064
$232$	−2.29010	−0.150352
$233$	7.46355	0.488953	0.244477	−	0.969655i	$-0.421384\pi$
$233$	7.46355	0.488953	0.244477	+	0.969655i	$0.421384\pi$
$234$	−3.60819	−0.235875
$235$	−1.49218	−0.0973392
$236$	−9.79527	−0.637618
$237$	−2.42944	−0.157809
$238$	10.4957	0.680336
$239$	−7.74748	−0.501143	−0.250571	−	0.968098i	$-0.580618\pi$
$239$	−7.74748	−0.501143	−0.250571	+	0.968098i	$0.580618\pi$
$240$	−0.706997	−0.0456365
$241$	1.98293	0.127731	0.0638657	−	0.997959i	$-0.479657\pi$
$241$	1.98293	0.127731	0.0638657	+	0.997959i	$0.479657\pi$
$242$	14.0436	0.902756
$243$	−15.0249	−0.963848
$244$	1.70579	0.109202
$245$	−2.78253	−0.177769
$246$	−1.88830	−0.120393
$247$	−0.267020	−0.0169901
$248$	−9.99830	−0.634893
$249$	−0.338156	−0.0214298
$250$	1.00000	0.0632456
$251$	−6.98470	−0.440870	−0.220435	−	0.975402i	$-0.570748\pi$
$251$	−6.98470	−0.440870	−0.220435	+	0.975402i	$0.570748\pi$
$252$	5.13444	0.323439
$253$	−12.2452	−0.769851
$254$	22.1156	1.38766
$255$	3.61330	0.226274
$256$	1.00000	0.0625000
$257$	6.46020	0.402976	0.201488	−	0.979491i	$-0.435422\pi$
$257$	6.46020	0.402976	0.201488	+	0.979491i	$0.435422\pi$
$258$	−2.02307	−0.125951
$259$	11.4658	0.712453
$260$	1.44319	0.0895026
$261$	5.72560	0.354405
$262$	−11.9713	−0.739589
$263$	−3.54780	−0.218767	−0.109383	−	0.994000i	$-0.534888\pi$
$263$	−3.54780	−0.218767	−0.109383	+	0.994000i	$0.534888\pi$
$264$	−3.53807	−0.217753
$265$	9.86709	0.606131
$266$	0.379968	0.0232973
$267$	5.09276	0.311672
$268$	−4.31306	−0.263462
$269$	−18.6251	−1.13559	−0.567797	−	0.823168i	$-0.692204\pi$
$269$	−18.6251	−1.13559	−0.567797	+	0.823168i	$0.692204\pi$
$270$	3.88859	0.236652
$271$	−5.90574	−0.358748	−0.179374	−	0.983781i	$-0.557407\pi$
$271$	−5.90574	−0.358748	−0.179374	+	0.983781i	$0.557407\pi$
$272$	−5.11077	−0.309886
$273$	2.09540	0.126819
$274$	−23.0925	−1.39507
$275$	5.00436	0.301774
$276$	1.72996	0.104131
$277$	−9.69772	−0.582680	−0.291340	−	0.956620i	$-0.594101\pi$
$277$	−9.69772	−0.582680	−0.291340	+	0.956620i	$0.594101\pi$
$278$	−13.6405	−0.818105
$279$	24.9973	1.49655
$280$	−2.05365	−0.122729
$281$	12.4748	0.744184	0.372092	−	0.928196i	$-0.378641\pi$
$281$	12.4748	0.744184	0.372092	+	0.928196i	$0.378641\pi$
$282$	1.05497	0.0628225
$283$	25.4177	1.51093	0.755463	−	0.655191i	$-0.227412\pi$
$283$	25.4177	1.51093	0.755463	+	0.655191i	$0.227412\pi$
$284$	−10.7214	−0.636196
$285$	0.130809	0.00774848
$286$	7.22222	0.427059
$287$	−5.48503	−0.323771
$288$	−2.50015	−0.147323
$289$	9.11996	0.536468
$290$	−2.29010	−0.134479
$291$	2.99124	0.175350
$292$	−1.68245	−0.0984579
$293$	−9.55180	−0.558022	−0.279011	−	0.960288i	$-0.590007\pi$
$293$	−9.55180	−0.558022	−0.279011	+	0.960288i	$0.590007\pi$
$294$	1.96724	0.114732
$295$	−9.79527	−0.570303
$296$	−5.58316	−0.324515
$297$	19.4599	1.12918
$298$	−1.26679	−0.0733834
$299$	−3.53135	−0.204223
$300$	−0.706997	−0.0408185
$301$	−5.87650	−0.338716
$302$	−8.57737	−0.493572
$303$	−2.98624	−0.171555
$304$	−0.185021	−0.0106117
$305$	1.70579	0.0976732
$306$	12.7777	0.730453
$307$	14.7147	0.839810	0.419905	−	0.907568i	$-0.362063\pi$
$307$	14.7147	0.839810	0.419905	+	0.907568i	$0.362063\pi$
$308$	−10.2772	−0.585597
$309$	0.886569	0.0504352
$310$	−9.99830	−0.567865
$311$	5.07781	0.287936	0.143968	−	0.989582i	$-0.454014\pi$
$311$	5.07781	0.287936	0.143968	+	0.989582i	$0.454014\pi$
$312$	−1.02033	−0.0577647
$313$	−4.59432	−0.259686	−0.129843	−	0.991535i	$-0.541447\pi$
$313$	−4.59432	−0.259686	−0.129843	+	0.991535i	$0.541447\pi$
$314$	−19.4496	−1.09761
$315$	5.13444	0.289293
$316$	3.43628	0.193306
$317$	−20.3855	−1.14496	−0.572482	−	0.819917i	$-0.694019\pi$
$317$	−20.3855	−1.14496	−0.572482	+	0.819917i	$0.694019\pi$
$318$	−6.97601	−0.391195
$319$	−11.4605	−0.641662
$320$	1.00000	0.0559017
$321$	−9.22502	−0.514890
$322$	5.02510	0.280038
$323$	0.945600	0.0526146
$324$	4.75124	0.263958
$325$	1.44319	0.0800536
$326$	−7.83300	−0.433830
$327$	2.55916	0.141522
$328$	2.67087	0.147474
$329$	3.06442	0.168947
$330$	−3.53807	−0.194764
$331$	10.6950	0.587851	0.293925	−	0.955828i	$-0.405038\pi$
$331$	10.6950	0.587851	0.293925	+	0.955828i	$0.405038\pi$
$332$	0.478299	0.0262501
$333$	13.9588	0.764936
$334$	11.9151	0.651963
$335$	−4.31306	−0.235648
$336$	1.45192	0.0792089
$337$	22.8677	1.24569	0.622843	−	0.782347i	$-0.285978\pi$
$337$	22.8677	1.24569	0.622843	+	0.782347i	$0.285978\pi$
$338$	−10.9172	−0.593818
$339$	−4.43855	−0.241069
$340$	−5.11077	−0.277170
$341$	−50.0351	−2.70955
$342$	0.462581	0.0250135
$343$	20.0899	1.08475
$344$	2.86150	0.154282
$345$	1.72996	0.0931380
$346$	7.26378	0.390503
$347$	16.6582	0.894258	0.447129	−	0.894469i	$-0.352446\pi$
$347$	16.6582	0.894258	0.447129	+	0.894469i	$0.352446\pi$
$348$	1.61909	0.0867924
$349$	−19.1618	−1.02571	−0.512853	−	0.858477i	$-0.671411\pi$
$349$	−19.1618	−1.02571	−0.512853	+	0.858477i	$0.671411\pi$
$350$	−2.05365	−0.109772
$351$	5.61197	0.299545
$352$	5.00436	0.266733
$353$	1.54088	0.0820128	0.0410064	−	0.999159i	$-0.486944\pi$
$353$	1.54088	0.0820128	0.0410064	+	0.999159i	$0.486944\pi$
$354$	6.92523	0.368072
$355$	−10.7214	−0.569031
$356$	−7.20336	−0.381777
$357$	−7.42045	−0.392732
$358$	−3.07473	−0.162505
$359$	36.2403	1.91269	0.956345	−	0.292240i	$-0.0944005\pi$
$359$	36.2403	1.91269	0.956345	+	0.292240i	$0.0944005\pi$
$360$	−2.50015	−0.131770
$361$	−18.9658	−0.998198
$362$	−14.2293	−0.747875
$363$	−9.92878	−0.521126
$364$	−2.96380	−0.155345
$365$	−1.68245	−0.0880634
$366$	−1.20599	−0.0630380
$367$	−34.0183	−1.77574	−0.887871	−	0.460092i	$-0.847817\pi$
$367$	−34.0183	−1.77574	−0.887871	+	0.460092i	$0.847817\pi$
$368$	−2.44691	−0.127554
$369$	−6.67759	−0.347621
$370$	−5.58316	−0.290255
$371$	−20.2635	−1.05203
$372$	7.06877	0.366499
$373$	−1.57188	−0.0813891	−0.0406945	−	0.999172i	$-0.512957\pi$
$373$	−1.57188	−0.0813891	−0.0406945	+	0.999172i	$0.512957\pi$
$374$	−25.5761	−1.32251
$375$	−0.706997	−0.0365092
$376$	−1.49218	−0.0769534
$377$	−3.30504	−0.170218
$378$	−7.98580	−0.410745
$379$	−17.1650	−0.881708	−0.440854	−	0.897579i	$-0.645324\pi$
$379$	−17.1650	−0.881708	−0.440854	+	0.897579i	$0.645324\pi$
$380$	−0.185021	−0.00949138
$381$	−15.6357	−0.801040
$382$	−26.0360	−1.33212
$383$	13.9245	0.711508	0.355754	−	0.934580i	$-0.384224\pi$
$383$	13.9245	0.711508	0.355754	+	0.934580i	$0.384224\pi$
$384$	−0.706997	−0.0360788
$385$	−10.2772	−0.523774
$386$	−15.7653	−0.802434
$387$	−7.15418	−0.363668
$388$	−4.23091	−0.214792
$389$	−21.5436	−1.09230	−0.546152	−	0.837686i	$-0.683908\pi$
$389$	−21.5436	−1.09230	−0.546152	+	0.837686i	$0.683908\pi$
$390$	−1.02033	−0.0516664
$391$	12.5056	0.632436
$392$	−2.78253	−0.140539
$393$	8.46367	0.426936
$394$	4.70772	0.237172
$395$	3.43628	0.172898
$396$	−12.5117	−0.628735
$397$	−25.0604	−1.25775	−0.628873	−	0.777508i	$-0.716484\pi$
$397$	−25.0604	−1.25775	−0.628873	+	0.777508i	$0.716484\pi$
$398$	−22.5777	−1.13172
$399$	−0.268636	−0.0134486
$400$	1.00000	0.0500000
$401$	9.66917	0.482855	0.241428	−	0.970419i	$-0.422384\pi$
$401$	9.66917	0.482855	0.241428	+	0.970419i	$0.422384\pi$
$402$	3.04932	0.152086
$403$	−14.4294	−0.718780
$404$	4.22384	0.210144
$405$	4.75124	0.236091
$406$	4.70305	0.233409
$407$	−27.9401	−1.38494
$408$	3.61330	0.178885
$409$	31.5033	1.55774	0.778869	−	0.627187i	$-0.215794\pi$
$409$	31.5033	1.55774	0.778869	+	0.627187i	$0.215794\pi$
$410$	2.67087	0.131905
$411$	16.3263	0.805318
$412$	−1.25399	−0.0617798
$413$	20.1160	0.989846
$414$	6.11766	0.300667
$415$	0.478299	0.0234788
$416$	1.44319	0.0707580
$417$	9.64382	0.472260
$418$	−0.925911	−0.0452878
$419$	29.8651	1.45900	0.729502	−	0.683978i	$-0.239752\pi$
$419$	29.8651	1.45900	0.729502	+	0.683978i	$0.239752\pi$
$420$	1.45192	0.0708466
$421$	−1.24282	−0.0605716	−0.0302858	−	0.999541i	$-0.509642\pi$
$421$	−1.24282	−0.0605716	−0.0302858	+	0.999541i	$0.509642\pi$
$422$	10.5796	0.515005
$423$	3.73069	0.181392
$424$	9.86709	0.479188
$425$	−5.11077	−0.247909
$426$	7.57998	0.367251
$427$	−3.50309	−0.169526
$428$	13.0482	0.630707
$429$	−5.10609	−0.246524
$430$	2.86150	0.137994
$431$	15.0924	0.726975	0.363488	−	0.931599i	$-0.381586\pi$
$431$	15.0924	0.726975	0.363488	+	0.931599i	$0.381586\pi$
$432$	3.88859	0.187090
$433$	19.3810	0.931392	0.465696	−	0.884945i	$-0.345804\pi$
$433$	19.3810	0.931392	0.465696	+	0.884945i	$0.345804\pi$
$434$	20.5330	0.985615
$435$	1.61909	0.0776295
$436$	−3.61976	−0.173355
$437$	0.452731	0.0216570
$438$	1.18949	0.0568359
$439$	20.4014	0.973705	0.486852	−	0.873484i	$-0.338145\pi$
$439$	20.4014	0.973705	0.486852	+	0.873484i	$0.338145\pi$
$440$	5.00436	0.238573
$441$	6.95676	0.331274
$442$	−7.37579	−0.350831
$443$	20.6581	0.981498	0.490749	−	0.871301i	$-0.336723\pi$
$443$	20.6581	0.981498	0.490749	+	0.871301i	$0.336723\pi$
$444$	3.94728	0.187330
$445$	−7.20336	−0.341472
$446$	2.98502	0.141345
$447$	0.895620	0.0423613
$448$	−2.05365	−0.0970257
$449$	24.9190	1.17600	0.588001	−	0.808860i	$-0.299915\pi$
$449$	24.9190	1.17600	0.588001	+	0.808860i	$0.299915\pi$
$450$	−2.50015	−0.117858
$451$	13.3660	0.629380
$452$	6.27803	0.295294
$453$	6.06418	0.284920
$454$	−0.464604	−0.0218049
$455$	−2.96380	−0.138945
$456$	0.130809	0.00612571
$457$	−13.7300	−0.642263	−0.321132	−	0.947035i	$-0.604063\pi$
$457$	−13.7300	−0.642263	−0.321132	+	0.947035i	$0.604063\pi$
$458$	5.74517	0.268454
$459$	−19.8737	−0.927625
$460$	−2.44691	−0.114088
$461$	−13.8355	−0.644385	−0.322193	−	0.946674i	$-0.604420\pi$
$461$	−13.8355	−0.644385	−0.322193	+	0.946674i	$0.604420\pi$
$462$	7.26594	0.338042
$463$	20.7694	0.965237	0.482618	−	0.875831i	$-0.339686\pi$
$463$	20.7694	0.965237	0.482618	+	0.875831i	$0.339686\pi$
$464$	−2.29010	−0.106315
$465$	7.06877	0.327806
$466$	7.46355	0.345742
$467$	−18.1859	−0.841545	−0.420772	−	0.907166i	$-0.638241\pi$
$467$	−18.1859	−0.841545	−0.420772	+	0.907166i	$0.638241\pi$
$468$	−3.60819	−0.166789
$469$	8.85751	0.409002
$470$	−1.49218	−0.0688292
$471$	13.7508	0.633605
$472$	−9.79527	−0.450864
$473$	14.3199	0.658432
$474$	−2.42944	−0.111588
$475$	−0.185021	−0.00848935
$476$	10.4957	0.481071
$477$	−24.6693	−1.12953
$478$	−7.74748	−0.354361
$479$	29.5437	1.34989	0.674944	−	0.737869i	$-0.264168\pi$
$479$	29.5437	1.34989	0.674944	+	0.737869i	$0.264168\pi$
$480$	−0.706997	−0.0322699
$481$	−8.05754	−0.367392
$482$	1.98293	0.0903198
$483$	−3.55273	−0.161655
$484$	14.0436	0.638345
$485$	−4.23091	−0.192116
$486$	−15.0249	−0.681543
$487$	1.39387	0.0631622	0.0315811	−	0.999501i	$-0.489946\pi$
$487$	1.39387	0.0631622	0.0315811	+	0.999501i	$0.489946\pi$
$488$	1.70579	0.0772175
$489$	5.53791	0.250433
$490$	−2.78253	−0.125702
$491$	−31.6266	−1.42729	−0.713643	−	0.700509i	$-0.752956\pi$
$491$	−31.6266	−1.42729	−0.713643	+	0.700509i	$0.752956\pi$
$492$	−1.88830	−0.0851310
$493$	11.7042	0.527129
$494$	−0.267020	−0.0120138
$495$	−12.5117	−0.562358
$496$	−9.99830	−0.448937
$497$	22.0179	0.987639
$498$	−0.338156	−0.0151531
$499$	11.7470	0.525867	0.262934	−	0.964814i	$-0.415310\pi$
$499$	11.7470	0.525867	0.262934	+	0.964814i	$0.415310\pi$
$500$	1.00000	0.0447214
$501$	−8.42391	−0.376353
$502$	−6.98470	−0.311742
$503$	0.853379	0.0380503	0.0190252	−	0.999819i	$-0.493944\pi$
$503$	0.853379	0.0380503	0.0190252	+	0.999819i	$0.493944\pi$
$504$	5.13444	0.228706
$505$	4.22384	0.187958
$506$	−12.2452	−0.544367
$507$	7.71844	0.342788
$508$	22.1156	0.981221
$509$	3.73108	0.165377	0.0826886	−	0.996575i	$-0.473649\pi$
$509$	3.73108	0.165377	0.0826886	+	0.996575i	$0.473649\pi$
$510$	3.61330	0.160000
$511$	3.45516	0.152847
$512$	1.00000	0.0441942
$513$	−0.719472	−0.0317655
$514$	6.46020	0.284947
$515$	−1.25399	−0.0552575
$516$	−2.02307	−0.0890607
$517$	−7.46741	−0.328416
$518$	11.4658	0.503781
$519$	−5.13547	−0.225422
$520$	1.44319	0.0632879
$521$	−5.79178	−0.253743	−0.126871	−	0.991919i	$-0.540494\pi$
$521$	−5.79178	−0.253743	−0.126871	+	0.991919i	$0.540494\pi$
$522$	5.72560	0.250602
$523$	18.2440	0.797753	0.398876	−	0.917005i	$-0.369400\pi$
$523$	18.2440	0.797753	0.398876	+	0.917005i	$0.369400\pi$
$524$	−11.9713	−0.522968
$525$	1.45192	0.0633671
$526$	−3.54780	−0.154691
$527$	51.0990	2.22591
$528$	−3.53807	−0.153975
$529$	−17.0126	−0.739679
$530$	9.86709	0.428599
$531$	24.4897	1.06276
$532$	0.379968	0.0164737
$533$	3.85456	0.166960
$534$	5.09276	0.220385
$535$	13.0482	0.564121
$536$	−4.31306	−0.186296
$537$	2.17383	0.0938075
$538$	−18.6251	−0.802987
$539$	−13.9248	−0.599783
$540$	3.88859	0.167338
$541$	17.8511	0.767478	0.383739	−	0.923442i	$-0.374636\pi$
$541$	17.8511	0.767478	0.383739	+	0.923442i	$0.374636\pi$
$542$	−5.90574	−0.253673
$543$	10.0601	0.431719
$544$	−5.11077	−0.219122
$545$	−3.61976	−0.155054
$546$	2.09540	0.0896747
$547$	−11.6106	−0.496432	−0.248216	−	0.968705i	$-0.579844\pi$
$547$	−11.6106	−0.496432	−0.248216	+	0.968705i	$0.579844\pi$
$548$	−23.0925	−0.986462
$549$	−4.26474	−0.182015
$550$	5.00436	0.213386
$551$	0.423716	0.0180509
$552$	1.72996	0.0736320
$553$	−7.05691	−0.300090
$554$	−9.69772	−0.412017
$555$	3.94728	0.167553
$556$	−13.6405	−0.578487
$557$	−0.0176112	−0.000746212 0	−0.000373106	−	1.00000i	$-0.500119\pi$
$557$	−0.0176112	−0.000746212 0	−0.000373106		1.00000i	$0.500119\pi$
$558$	24.9973	1.05822
$559$	4.12967	0.174666
$560$	−2.05365	−0.0867825
$561$	18.0822	0.763433
$562$	12.4748	0.526218
$563$	−0.574818	−0.0242257	−0.0121129	−	0.999927i	$-0.503856\pi$
$563$	−0.574818	−0.0242257	−0.0121129	+	0.999927i	$0.503856\pi$
$564$	1.05497	0.0444222
$565$	6.27803	0.264119
$566$	25.4177	1.06839
$567$	−9.75737	−0.409771
$568$	−10.7214	−0.449859
$569$	40.5272	1.69899	0.849495	−	0.527596i	$-0.176907\pi$
$569$	40.5272	1.69899	0.849495	+	0.527596i	$0.176907\pi$
$570$	0.130809	0.00547900
$571$	4.62409	0.193512	0.0967561	−	0.995308i	$-0.469153\pi$
$571$	4.62409	0.193512	0.0967561	+	0.995308i	$0.469153\pi$
$572$	7.22222	0.301976
$573$	18.4074	0.768979
$574$	−5.48503	−0.228941
$575$	−2.44691	−0.102043
$576$	−2.50015	−0.104173
$577$	−13.2880	−0.553189	−0.276594	−	0.960987i	$-0.589206\pi$
$577$	−13.2880	−0.553189	−0.276594	+	0.960987i	$0.589206\pi$
$578$	9.11996	0.379340
$579$	11.1460	0.463214
$580$	−2.29010	−0.0950911
$581$	−0.982257	−0.0407509
$582$	2.99124	0.123991
$583$	49.3785	2.04505
$584$	−1.68245	−0.0696203
$585$	−3.60819	−0.149180
$586$	−9.55180	−0.394581
$587$	−30.1623	−1.24493	−0.622466	−	0.782647i	$-0.713869\pi$
$587$	−30.1623	−1.24493	−0.622466	+	0.782647i	$0.713869\pi$
$588$	1.96724	0.0811277
$589$	1.84990	0.0762236
$590$	−9.79527	−0.403265
$591$	−3.32835	−0.136910
$592$	−5.58316	−0.229467
$593$	−15.0331	−0.617337	−0.308668	−	0.951170i	$-0.599883\pi$
$593$	−15.0331	−0.617337	−0.308668	+	0.951170i	$0.599883\pi$
$594$	19.4599	0.798450
$595$	10.4957	0.430283
$596$	−1.26679	−0.0518899
$597$	15.9624	0.653296
$598$	−3.53135	−0.144408
$599$	3.79170	0.154925	0.0774623	−	0.996995i	$-0.475318\pi$
$599$	3.79170	0.154925	0.0774623	+	0.996995i	$0.475318\pi$
$600$	−0.706997	−0.0288630
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−5.87650	−0.239508
$603$	10.7833	0.439131
$604$	−8.57737	−0.349008
$605$	14.0436	0.570953
$606$	−2.98624	−0.121308
$607$	−34.5176	−1.40103	−0.700513	−	0.713639i	$-0.747046\pi$
$607$	−34.5176	−1.40103	−0.700513	+	0.713639i	$0.747046\pi$
$608$	−0.185021	−0.00750359
$609$	−3.32504	−0.134738
$610$	1.70579	0.0690654
$611$	−2.15350	−0.0871212
$612$	12.7777	0.516509
$613$	−13.7687	−0.556114	−0.278057	−	0.960565i	$-0.589690\pi$
$613$	−13.7687	−0.556114	−0.278057	+	0.960565i	$0.589690\pi$
$614$	14.7147	0.593835
$615$	−1.88830	−0.0761435
$616$	−10.2772	−0.414080
$617$	7.91563	0.318671	0.159336	−	0.987224i	$-0.449065\pi$
$617$	7.91563	0.318671	0.159336	+	0.987224i	$0.449065\pi$
$618$	0.886569	0.0356630
$619$	22.9512	0.922487	0.461243	−	0.887274i	$-0.347404\pi$
$619$	22.9512	0.922487	0.461243	+	0.887274i	$0.347404\pi$
$620$	−9.99830	−0.401541
$621$	−9.51505	−0.381826
$622$	5.07781	0.203602
$623$	14.7932	0.592676
$624$	−1.02033	−0.0408458
$625$	1.00000	0.0400000
$626$	−4.59432	−0.183626
$627$	0.654617	0.0261429
$628$	−19.4496	−0.776124
$629$	28.5343	1.13774
$630$	5.13444	0.204561
$631$	−29.6919	−1.18201	−0.591007	−	0.806666i	$-0.701270\pi$
$631$	−29.6919	−1.18201	−0.591007	+	0.806666i	$0.701270\pi$
$632$	3.43628	0.136688
$633$	−7.47971	−0.297292
$634$	−20.3855	−0.809612
$635$	22.1156	0.877631
$636$	−6.97601	−0.276617
$637$	−4.01571	−0.159108
$638$	−11.4605	−0.453724
$639$	26.8051	1.06039
$640$	1.00000	0.0395285
$641$	−23.7718	−0.938931	−0.469465	−	0.882951i	$-0.655553\pi$
$641$	−23.7718	−0.938931	−0.469465	+	0.882951i	$0.655553\pi$
$642$	−9.22502	−0.364082
$643$	−26.0809	−1.02853	−0.514266	−	0.857631i	$-0.671936\pi$
$643$	−26.0809	−1.02853	−0.514266	+	0.857631i	$0.671936\pi$
$644$	5.02510	0.198017
$645$	−2.02307	−0.0796583
$646$	0.945600	0.0372041
$647$	38.8577	1.52765	0.763827	−	0.645421i	$-0.223318\pi$
$647$	38.8577	1.52765	0.763827	+	0.645421i	$0.223318\pi$
$648$	4.75124	0.186646
$649$	−49.0190	−1.92417
$650$	1.44319	0.0566064
$651$	−14.5168	−0.568957
$652$	−7.83300	−0.306764
$653$	12.7761	0.499967	0.249984	−	0.968250i	$-0.419575\pi$
$653$	12.7761	0.499967	0.249984	+	0.968250i	$0.419575\pi$
$654$	2.55916	0.100071
$655$	−11.9713	−0.467757
$656$	2.67087	0.104280
$657$	4.20638	0.164107
$658$	3.06442	0.119463
$659$	2.00349	0.0780449	0.0390225	−	0.999238i	$-0.487576\pi$
$659$	2.00349	0.0780449	0.0390225	+	0.999238i	$0.487576\pi$
$660$	−3.53807	−0.137719
$661$	−25.2346	−0.981510	−0.490755	−	0.871298i	$-0.663279\pi$
$661$	−25.2346	−0.981510	−0.490755	+	0.871298i	$0.663279\pi$
$662$	10.6950	0.415673
$663$	5.21466	0.202521
$664$	0.478299	0.0185616
$665$	0.379968	0.0147345
$666$	13.9588	0.540891
$667$	5.60367	0.216975
$668$	11.9151	0.461007
$669$	−2.11040	−0.0815927
$670$	−4.31306	−0.166628
$671$	8.53638	0.329543
$672$	1.45192	0.0560092
$673$	−22.6212	−0.871985	−0.435992	−	0.899950i	$-0.643603\pi$
$673$	−22.6212	−0.871985	−0.435992	+	0.899950i	$0.643603\pi$
$674$	22.8677	0.880833
$675$	3.88859	0.149672
$676$	−10.9172	−0.419893
$677$	−31.7848	−1.22159	−0.610795	−	0.791789i	$-0.709150\pi$
$677$	−31.7848	−1.22159	−0.610795	+	0.791789i	$0.709150\pi$
$678$	−4.43855	−0.170462
$679$	8.68880	0.333446
$680$	−5.11077	−0.195989
$681$	0.328473	0.0125871
$682$	−50.0351	−1.91594
$683$	10.5366	0.403172	0.201586	−	0.979471i	$-0.435390\pi$
$683$	10.5366	0.403172	0.201586	+	0.979471i	$0.435390\pi$
$684$	0.462581	0.0176872
$685$	−23.0925	−0.882319
$686$	20.0899	0.767035
$687$	−4.06182	−0.154968
$688$	2.86150	0.109094
$689$	14.2401	0.542503
$690$	1.72996	0.0658585
$691$	40.7628	1.55069	0.775345	−	0.631538i	$-0.217576\pi$
$691$	40.7628	1.55069	0.775345	+	0.631538i	$0.217576\pi$
$692$	7.26378	0.276127
$693$	25.6946	0.976056
$694$	16.6582	0.632336
$695$	−13.6405	−0.517415
$696$	1.61909	0.0613715
$697$	−13.6502	−0.517038
$698$	−19.1618	−0.725283
$699$	−5.27671	−0.199583
$700$	−2.05365	−0.0776206
$701$	−33.0731	−1.24916	−0.624578	−	0.780963i	$-0.714729\pi$
$701$	−33.0731	−1.24916	−0.624578	+	0.780963i	$0.714729\pi$
$702$	5.61197	0.211810
$703$	1.03300	0.0389604
$704$	5.00436	0.188609
$705$	1.05497	0.0397324
$706$	1.54088	0.0579918
$707$	−8.67428	−0.326230
$708$	6.92523	0.260266
$709$	9.66820	0.363097	0.181548	−	0.983382i	$-0.441889\pi$
$709$	9.66820	0.363097	0.181548	+	0.983382i	$0.441889\pi$
$710$	−10.7214	−0.402366
$711$	−8.59123	−0.322196
$712$	−7.20336	−0.269957
$713$	24.4650	0.916220
$714$	−7.42045	−0.277703
$715$	7.22222	0.270096
$716$	−3.07473	−0.114908
$717$	5.47744	0.204559
$718$	36.2403	1.35248
$719$	−36.2264	−1.35102	−0.675508	−	0.737353i	$-0.736076\pi$
$719$	−36.2264	−1.35102	−0.675508	+	0.737353i	$0.736076\pi$
$720$	−2.50015	−0.0931753
$721$	2.57526	0.0959076
$722$	−18.9658	−0.705833
$723$	−1.40192	−0.0521381
$724$	−14.2293	−0.528827
$725$	−2.29010	−0.0850520
$726$	−9.92878	−0.368491
$727$	23.9662	0.888859	0.444429	−	0.895814i	$-0.353406\pi$
$727$	23.9662	0.888859	0.444429	+	0.895814i	$0.353406\pi$
$728$	−2.96380	−0.109846
$729$	−3.63116	−0.134487
$730$	−1.68245	−0.0622703
$731$	−14.6244	−0.540905
$732$	−1.20599	−0.0445746
$733$	47.4317	1.75193	0.875965	−	0.482374i	$-0.160225\pi$
$733$	47.4317	1.75193	0.875965	+	0.482374i	$0.160225\pi$
$734$	−34.0183	−1.25564
$735$	1.96724	0.0725628
$736$	−2.44691	−0.0901944
$737$	−21.5841	−0.795060
$738$	−6.67759	−0.245805
$739$	−13.1939	−0.485347	−0.242674	−	0.970108i	$-0.578024\pi$
$739$	−13.1939	−0.485347	−0.242674	+	0.970108i	$0.578024\pi$
$740$	−5.58316	−0.205241
$741$	0.188782	0.00693509
$742$	−20.2635	−0.743898
$743$	24.6000	0.902488	0.451244	−	0.892401i	$-0.350980\pi$
$743$	24.6000	0.902488	0.451244	+	0.892401i	$0.350980\pi$
$744$	7.06877	0.259154
$745$	−1.26679	−0.0464117
$746$	−1.57188	−0.0575508
$747$	−1.19582	−0.0437528
$748$	−25.5761	−0.935155
$749$	−26.7963	−0.979117
$750$	−0.706997	−0.0258159
$751$	−6.01528	−0.219501	−0.109750	−	0.993959i	$-0.535005\pi$
$751$	−6.01528	−0.219501	−0.109750	+	0.993959i	$0.535005\pi$
$752$	−1.49218	−0.0544143
$753$	4.93816	0.179957
$754$	−3.30504	−0.120362
$755$	−8.57737	−0.312163
$756$	−7.98580	−0.290441
$757$	13.2749	0.482485	0.241242	−	0.970465i	$-0.422445\pi$
$757$	13.2749	0.482485	0.241242	+	0.970465i	$0.422445\pi$
$758$	−17.1650	−0.623461
$759$	8.65734	0.314242
$760$	−0.185021	−0.00671142
$761$	21.9055	0.794072	0.397036	−	0.917803i	$-0.370039\pi$
$761$	21.9055	0.794072	0.397036	+	0.917803i	$0.370039\pi$
$762$	−15.6357	−0.566421
$763$	7.43372	0.269119
$764$	−26.0360	−0.941949
$765$	12.7777	0.461979
$766$	13.9245	0.503112
$767$	−14.1364	−0.510436
$768$	−0.706997	−0.0255116
$769$	−45.5916	−1.64408	−0.822038	−	0.569433i	$-0.807163\pi$
$769$	−45.5916	−1.64408	−0.822038	+	0.569433i	$0.807163\pi$
$770$	−10.2772	−0.370364
$771$	−4.56734	−0.164489
$772$	−15.7653	−0.567407
$773$	7.18395	0.258389	0.129194	−	0.991619i	$-0.458761\pi$
$773$	7.18395	0.258389	0.129194	+	0.991619i	$0.458761\pi$
$774$	−7.15418	−0.257152
$775$	−9.99830	−0.359150
$776$	−4.23091	−0.151881
$777$	−8.10632	−0.290813
$778$	−21.5436	−0.772376
$779$	−0.494167	−0.0177054
$780$	−1.02033	−0.0365336
$781$	−53.6536	−1.91988
$782$	12.5056	0.447200
$783$	−8.90526	−0.318248
$784$	−2.78253	−0.0993761
$785$	−19.4496	−0.694187
$786$	8.46367	0.301889
$787$	3.09512	0.110329	0.0551645	−	0.998477i	$-0.482432\pi$
$787$	3.09512	0.110329	0.0551645	+	0.998477i	$0.482432\pi$
$788$	4.70772	0.167706
$789$	2.50828	0.0892972
$790$	3.43628	0.122257
$791$	−12.8929	−0.458418
$792$	−12.5117	−0.444583
$793$	2.46177	0.0874201
$794$	−25.0604	−0.889361
$795$	−6.97601	−0.247414
$796$	−22.5777	−0.800245
$797$	−26.6893	−0.945384	−0.472692	−	0.881228i	$-0.656718\pi$
$797$	−26.6893	−0.945384	−0.472692	+	0.881228i	$0.656718\pi$
$798$	−0.268636	−0.00950963
$799$	7.62620	0.269796
$800$	1.00000	0.0353553
$801$	18.0095	0.636335
$802$	9.66917	0.341430
$803$	−8.41958	−0.297120
$804$	3.04932	0.107541
$805$	5.02510	0.177111
$806$	−14.4294	−0.508254
$807$	13.1679	0.463533
$808$	4.22384	0.148594
$809$	3.03665	0.106763	0.0533815	−	0.998574i	$-0.483000\pi$
$809$	3.03665	0.106763	0.0533815	+	0.998574i	$0.483000\pi$
$810$	4.75124	0.166942
$811$	−19.1322	−0.671822	−0.335911	−	0.941894i	$-0.609044\pi$
$811$	−19.1322	−0.671822	−0.335911	+	0.941894i	$0.609044\pi$
$812$	4.70305	0.165045
$813$	4.17534	0.146436
$814$	−27.9401	−0.979301
$815$	−7.83300	−0.274378
$816$	3.61330	0.126491
$817$	−0.529437	−0.0185227
$818$	31.5033	1.10149
$819$	7.40995	0.258925
$820$	2.67087	0.0932708
$821$	41.5636	1.45058	0.725290	−	0.688443i	$-0.241706\pi$
$821$	41.5636	1.45058	0.725290	+	0.688443i	$0.241706\pi$
$822$	16.3263	0.569446
$823$	7.20870	0.251280	0.125640	−	0.992076i	$-0.459902\pi$
$823$	7.20870	0.251280	0.125640	+	0.992076i	$0.459902\pi$
$824$	−1.25399	−0.0436849
$825$	−3.53807	−0.123180
$826$	20.1160	0.699926
$827$	26.3246	0.915397	0.457698	−	0.889108i	$-0.348674\pi$
$827$	26.3246	0.915397	0.457698	+	0.889108i	$0.348674\pi$
$828$	6.11766	0.212603
$829$	−17.0067	−0.590667	−0.295334	−	0.955394i	$-0.595431\pi$
$829$	−17.0067	−0.590667	−0.295334	+	0.955394i	$0.595431\pi$
$830$	0.478299	0.0166020
$831$	6.85626	0.237841
$832$	1.44319	0.0500335
$833$	14.2209	0.492724
$834$	9.64382	0.333938
$835$	11.9151	0.412337
$836$	−0.925911	−0.0320233
$837$	−38.8793	−1.34387
$838$	29.8651	1.03167
$839$	48.0681	1.65950	0.829748	−	0.558138i	$-0.188484\pi$
$839$	48.0681	1.65950	0.829748	+	0.558138i	$0.188484\pi$
$840$	1.45192	0.0500961
$841$	−23.7555	−0.819154
$842$	−1.24282	−0.0428306
$843$	−8.81965	−0.303765
$844$	10.5796	0.364163
$845$	−10.9172	−0.375564
$846$	3.73069	0.128264
$847$	−28.8406	−0.990974
$848$	9.86709	0.338837
$849$	−17.9703	−0.616738
$850$	−5.11077	−0.175298
$851$	13.6615	0.468311
$852$	7.57998	0.259686
$853$	−36.5741	−1.25227	−0.626137	−	0.779713i	$-0.715365\pi$
$853$	−36.5741	−1.25227	−0.626137	+	0.779713i	$0.715365\pi$
$854$	−3.50309	−0.119873
$855$	0.462581	0.0158199
$856$	13.0482	0.445977
$857$	−4.13912	−0.141390	−0.0706948	−	0.997498i	$-0.522522\pi$
$857$	−4.13912	−0.141390	−0.0706948	+	0.997498i	$0.522522\pi$
$858$	−5.10609	−0.174319
$859$	38.0715	1.29898	0.649491	−	0.760369i	$-0.274982\pi$
$859$	38.0715	1.29898	0.649491	+	0.760369i	$0.274982\pi$
$860$	2.86150	0.0975762
$861$	3.87790	0.132158
$862$	15.0924	0.514049
$863$	23.5948	0.803178	0.401589	−	0.915820i	$-0.368458\pi$
$863$	23.5948	0.803178	0.401589	+	0.915820i	$0.368458\pi$
$864$	3.88859	0.132293
$865$	7.26378	0.246976
$866$	19.3810	0.658593
$867$	−6.44779	−0.218978
$868$	20.5330	0.696935
$869$	17.1964	0.583347
$870$	1.61909	0.0548924
$871$	−6.22455	−0.210911
$872$	−3.61976	−0.122581
$873$	10.5779	0.358009
$874$	0.452731	0.0153138
$875$	−2.05365	−0.0694260
$876$	1.18949	0.0401891
$877$	−25.7086	−0.868119	−0.434060	−	0.900884i	$-0.642919\pi$
$877$	−25.7086	−0.868119	−0.434060	+	0.900884i	$0.642919\pi$
$878$	20.4014	0.688513
$879$	6.75310	0.227776
$880$	5.00436	0.168697
$881$	27.1414	0.914417	0.457209	−	0.889359i	$-0.348849\pi$
$881$	27.1414	0.914417	0.457209	+	0.889359i	$0.348849\pi$
$882$	6.95676	0.234246
$883$	6.73581	0.226678	0.113339	−	0.993556i	$-0.463845\pi$
$883$	6.73581	0.226678	0.113339	+	0.993556i	$0.463845\pi$
$884$	−7.37579	−0.248075
$885$	6.92523	0.232789
$886$	20.6581	0.694024
$887$	23.6715	0.794810	0.397405	−	0.917643i	$-0.369911\pi$
$887$	23.6715	0.794810	0.397405	+	0.917643i	$0.369911\pi$
$888$	3.94728	0.132462
$889$	−45.4177	−1.52326
$890$	−7.20336	−0.241457
$891$	23.7769	0.796556
$892$	2.98502	0.0999458
$893$	0.276085	0.00923884
$894$	0.895620	0.0299540
$895$	−3.07473	−0.102777
$896$	−2.05365	−0.0686076
$897$	2.49666	0.0833609
$898$	24.9190	0.831558
$899$	22.8971	0.763660
$900$	−2.50015	−0.0833385
$901$	−50.4284	−1.68001
$902$	13.3660	0.445039
$903$	4.15467	0.138259
$904$	6.27803	0.208804
$905$	−14.2293	−0.472998
$906$	6.06418	0.201469
$907$	11.6296	0.386155	0.193078	−	0.981183i	$-0.438153\pi$
$907$	11.6296	0.386155	0.193078	+	0.981183i	$0.438153\pi$
$908$	−0.464604	−0.0154184
$909$	−10.5603	−0.350261
$910$	−2.96380	−0.0982489
$911$	−11.6634	−0.386426	−0.193213	−	0.981157i	$-0.561891\pi$
$911$	−11.6634	−0.386426	−0.193213	+	0.981157i	$0.561891\pi$
$912$	0.130809	0.00433153
$913$	2.39358	0.0792158
$914$	−13.7300	−0.454149
$915$	−1.20599	−0.0398688
$916$	5.74517	0.189826
$917$	24.5848	0.811862
$918$	−19.8737	−0.655930
$919$	−6.75251	−0.222745	−0.111372	−	0.993779i	$-0.535525\pi$
$919$	−6.75251	−0.222745	−0.111372	+	0.993779i	$0.535525\pi$
$920$	−2.44691	−0.0806724
$921$	−10.4032	−0.342798
$922$	−13.8355	−0.455649
$923$	−15.4729	−0.509298
$924$	7.26594	0.239032
$925$	−5.58316	−0.183573
$926$	20.7694	0.682525
$927$	3.13518	0.102973
$928$	−2.29010	−0.0751761
$929$	−9.97770	−0.327358	−0.163679	−	0.986514i	$-0.552336\pi$
$929$	−9.97770	−0.327358	−0.163679	+	0.986514i	$0.552336\pi$
$930$	7.06877	0.231794
$931$	0.514827	0.0168728
$932$	7.46355	0.244477
$933$	−3.59000	−0.117531
$934$	−18.1859	−0.595062
$935$	−25.5761	−0.836428
$936$	−3.60819	−0.117937
$937$	41.3109	1.34957	0.674785	−	0.738015i	$-0.264237\pi$
$937$	41.3109	1.34957	0.674785	+	0.738015i	$0.264237\pi$
$938$	8.85751	0.289208
$939$	3.24817	0.106000
$940$	−1.49218	−0.0486696
$941$	42.5318	1.38650	0.693249	−	0.720699i	$-0.256179\pi$
$941$	42.5318	1.38650	0.693249	+	0.720699i	$0.256179\pi$
$942$	13.7508	0.448026
$943$	−6.53539	−0.212822
$944$	−9.79527	−0.318809
$945$	−7.98580	−0.259778
$946$	14.3199	0.465582
$947$	24.1694	0.785399	0.392700	−	0.919667i	$-0.371541\pi$
$947$	24.1694	0.785399	0.392700	+	0.919667i	$0.371541\pi$
$948$	−2.42944	−0.0789046
$949$	−2.42809	−0.0788191
$950$	−0.185021	−0.00600288
$951$	14.4125	0.467357
$952$	10.4957	0.340168
$953$	−39.9170	−1.29304	−0.646519	−	0.762898i	$-0.723776\pi$
$953$	−39.9170	−1.29304	−0.646519	+	0.762898i	$0.723776\pi$
$954$	−24.6693	−0.798697
$955$	−26.0360	−0.842505
$956$	−7.74748	−0.250571
$957$	8.10251	0.261917
$958$	29.5437	0.954514
$959$	47.4238	1.53140
$960$	−0.706997	−0.0228182
$961$	68.9660	2.22471
$962$	−8.05754	−0.259786
$963$	−32.6224	−1.05124
$964$	1.98293	0.0638657
$965$	−15.7653	−0.507504
$966$	−3.55273	−0.114307
$967$	32.3808	1.04130	0.520648	−	0.853771i	$-0.325690\pi$
$967$	32.3808	1.04130	0.520648	+	0.853771i	$0.325690\pi$
$968$	14.0436	0.451378
$969$	−0.668537	−0.0214765
$970$	−4.23091	−0.135846
$971$	1.62327	0.0520931	0.0260465	−	0.999661i	$-0.491708\pi$
$971$	1.62327	0.0520931	0.0260465	+	0.999661i	$0.491708\pi$
$972$	−15.0249	−0.481924
$973$	28.0129	0.898051
$974$	1.39387	0.0446624
$975$	−1.02033	−0.0326767
$976$	1.70579	0.0546010
$977$	26.7430	0.855585	0.427792	−	0.903877i	$-0.359291\pi$
$977$	26.7430	0.855585	0.427792	+	0.903877i	$0.359291\pi$
$978$	5.53791	0.177083
$979$	−36.0482	−1.15210
$980$	−2.78253	−0.0888847
$981$	9.04997	0.288943
$982$	−31.6266	−1.00924
$983$	29.2734	0.933677	0.466839	−	0.884342i	$-0.345393\pi$
$983$	29.2734	0.933677	0.466839	+	0.884342i	$0.345393\pi$
$984$	−1.88830	−0.0601967
$985$	4.70772	0.150000
$986$	11.7042	0.372736
$987$	−2.16653	−0.0689616
$988$	−0.267020	−0.00849503
$989$	−7.00183	−0.222645
$990$	−12.5117	−0.397647
$991$	32.0354	1.01764	0.508820	−	0.860873i	$-0.330082\pi$
$991$	32.0354	1.01764	0.508820	+	0.860873i	$0.330082\pi$
$992$	−9.99830	−0.317446
$993$	−7.56134	−0.239952
$994$	22.0179	0.698366
$995$	−22.5777	−0.715761
$996$	−0.338156	−0.0107149
$997$	32.2423	1.02113	0.510563	−	0.859841i	$-0.329437\pi$
$997$	32.2423	1.02113	0.510563	+	0.859841i	$0.329437\pi$
$998$	11.7470	0.371844
$999$	−21.7107	−0.686895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.8	✓	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.706997 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.706997 q^{6} -2.05365 q^{7} +1.00000 q^{8} -2.50015 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.706997 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.706997 q^{6} -2.05365 q^{7} +1.00000 q^{8} -2.50015 q^{9} +1.00000 q^{10} +5.00436 q^{11} -0.706997 q^{12} +1.44319 q^{13} -2.05365 q^{14} -0.706997 q^{15} +1.00000 q^{16} -5.11077 q^{17} -2.50015 q^{18} -0.185021 q^{19} +1.00000 q^{20} +1.45192 q^{21} +5.00436 q^{22} -2.44691 q^{23} -0.706997 q^{24} +1.00000 q^{25} +1.44319 q^{26} +3.88859 q^{27} -2.05365 q^{28} -2.29010 q^{29} -0.706997 q^{30} -9.99830 q^{31} +1.00000 q^{32} -3.53807 q^{33} -5.11077 q^{34} -2.05365 q^{35} -2.50015 q^{36} -5.58316 q^{37} -0.185021 q^{38} -1.02033 q^{39} +1.00000 q^{40} +2.67087 q^{41} +1.45192 q^{42} +2.86150 q^{43} +5.00436 q^{44} -2.50015 q^{45} -2.44691 q^{46} -1.49218 q^{47} -0.706997 q^{48} -2.78253 q^{49} +1.00000 q^{50} +3.61330 q^{51} +1.44319 q^{52} +9.86709 q^{53} +3.88859 q^{54} +5.00436 q^{55} -2.05365 q^{56} +0.130809 q^{57} -2.29010 q^{58} -9.79527 q^{59} -0.706997 q^{60} +1.70579 q^{61} -9.99830 q^{62} +5.13444 q^{63} +1.00000 q^{64} +1.44319 q^{65} -3.53807 q^{66} -4.31306 q^{67} -5.11077 q^{68} +1.72996 q^{69} -2.05365 q^{70} -10.7214 q^{71} -2.50015 q^{72} -1.68245 q^{73} -5.58316 q^{74} -0.706997 q^{75} -0.185021 q^{76} -10.2772 q^{77} -1.02033 q^{78} +3.43628 q^{79} +1.00000 q^{80} +4.75124 q^{81} +2.67087 q^{82} +0.478299 q^{83} +1.45192 q^{84} -5.11077 q^{85} +2.86150 q^{86} +1.61909 q^{87} +5.00436 q^{88} -7.20336 q^{89} -2.50015 q^{90} -2.96380 q^{91} -2.44691 q^{92} +7.06877 q^{93} -1.49218 q^{94} -0.185021 q^{95} -0.706997 q^{96} -4.23091 q^{97} -2.78253 q^{98} -12.5117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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